1. Field of the Invention
The present invention generally relates to method, system and computer program product used in engineering analysis, more particularly to numerical simulation of the non-linear structural behaviors of a general three-dimensional (3-D) shell structures based on mesh-free analysis.
2. Description of the Related Art
Finite element analysis (FEA) is a computerized method widely used in industry to model and solve engineering problems relating to complex systems since its invention in late 1950's. With the advent of the modern digital computer, FEA has been implemented as FEA computer program product. Basically, the FEA computer program product is provided with a model of the geometric description and the associated material properties at each point within the model. In this model, the geometry of the system under analysis is represented by solids, shells and beams of various sizes, which are called elements. The vertices of the elements are referred to as nodes. The individual elements are connected together by a topological map, which is usually called mesh. The model is comprised of a finite number of elements, which are assigned a material name to associate with material properties. The model thus represents the physical space occupied by the object under analysis along with its immediate surroundings. The FEA computer program product then refers to a table in which the properties (e.g., stress-strain constitutive equation, Young's modulus, Poisson's ratio, thermo-conductivity) of each material type are tabulated. Additionally, the conditions at the boundary of the object (i.e., loadings, physical constraints, etc.) are specified. In this fashion a model of the object and its environment is created.
FEA computer program product can be classified into two general types, implicit analysis computer program product and explicit analysis computer program product. The implicit analysis computer program product uses an implicit equation solver to solve a system of coupled linear equations. Such computer program product is generally used to simulate static or quasi-static problems. Explicit computer program product does not solve coupled equations but explicitly solves for each unknown assuming them uncoupled. The explicit analysis computer program product usually uses central difference time integration which requires very small solution cycles or time steps for the method to be stable and accurate. The explicit analysis computer program product is generally used to simulate short duration events where dynamics are important such as impact type events.
Although FEA has been successfully applied to many fields to simulate various engineering problems, there are some instances that FEA may not be advantageous due to numerical compatibility condition is not the same as the physical compatibility condition of a continuum. For example, in Lagrangian type of computations, one may experience mesh distortion, which can either end the computation altogether or result in dramatic deterioration of accuracy. In addition, the FEA often requires a very fine mesh in problems with high gradients or a distinct local character, which can be computationally expensive. For this reason, adaptive FEA has been developed.
Adaptive re-meshing procedures for simulations of impact/penetration problems, explosion/fragmentation problems, flow pass obstacles, and fluid-structure interaction problems etc., have become formidable tasks to undertake. The difficulties here are not only re-meshing, but also mapping the state variables from the old mesh to the new mesh. Hence, this process often introduces numerical errors; frequent re-mesh is not desirable. Another procedure called Arbitrary Lagrangian Eulerian (ALE) formulations has been developed. Its objective is to move the mesh independently of the material so that the mesh distortion can be minimized. Unfortunately, the mesh distortion still creates severe numerical errors for very large strain and high speed mechanical simulations. In other cases, a mesh may carry inherent bias in numerical simulations, and its presence becomes a nuisance in computations. An example is the strain localization problem, which is notorious for its mesh alignment sensitivity. Therefore it is computationally efficacious to discretize a continuum by a set of nodal points without mesh constraints.
The mesh-free analysis has become one of the focused research topics during the 1990's. Many applications of using mesh-free analysis have been achieved in the past decade. Today, the vast majority of the engineering applications using mesh-free analysis are related to two-(2-D) and three-dimensional (3-D) solid structures. It is well known amongst the skilled in the art of engineering analysis that the mesh-free analysis would not be practical if the mesh-free analysis could only handle solid structures. Many of the mechanical structures contain shells or plates such as the structure and the components of an automobile. Therefore, it would be desirable to have the capability to analyze to a general 3-D shell structures using mesh-free analysis. In particular, it would be extremely desirable for the mesh-free analysis to handle shell structure involving material and geometrical non-linearity.